Many bettas end up with torn fins or even bite their own fins as they're being shipped to the pet store. The way to tell if it is a simple rip or if it's fin rot is by carefully looking at the edge--if it is crusty, fuzzy, black or gray, then it is likely infected. If there is no change in color or texture, or if the edge is clear or whitish (a sign of healthy new fin growth) he is fine. In any case, the best thing to do is keep the water pristinely clean. You could add a little aquarium salt. With clean water it will heal on its own. Do not add anything like bettafix or melafix--they contain an ingredient called melaleuca which has been shown to harm the labyrinth organ in bettas as well as other anabantoids.
As for the color--is the tank heated with an adjustable heater? Bettas need constant stable temperatures of 78-83 degrees to be comfortable, healthy, and active. Bettas kept in lower temperatures tend to be pale, lethargic, and have issues with circulation and digestion. They will also heal more slowly in colder water. If the water is not stable, it will cause them to become very weak and susceptible to infection and parasite infestation. If there is an incandescent light on the aquarium, you should replace it with a fluorescent bulb, if you cannot--then you should never turn the incandescent light on. They get very hot and cause dangerous temperature changes.
Also, if the fish has inadequate hiding places in the tank, they can become very stressed out and pale. I suggest adding some silk plants with large leaves he can hide behind. Once he is warm and feels secure, he should color up and be a much happier fish.